Method and a system for detecting communication relaying network elements

ABSTRACT

A method for determining if a signal received at a radio receiver in a communication system is transmitted to the receiver via a direct radio link comprising the steps of: determining a signal characteristic based on one or more signal measurements collected at the receiver; comparing the signal characteristic as determined with at least one predetermined system parameter; and responsive to said comparison determining if said signal is received via a direct link.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a National Phase of International Application No.PCT/JB2002/04590 filed on Oct. 30, 2002. the entire disclosure of whichis incorporated herein by reference, which claims the benefit of GreatBritain Patent Application No. 0126267.4 that was filed Nov. 1, 2001,the entire disclosure of which is incorporated herein by reference.

The present invention relates to a method and apparatus for determiningif a signal received by a mobile user equipment in a communicationsystem is transmitted via a direct or indirect communication link. Inparticular, but not exclusively, the method and apparatus can beutilized to enable location services in the communication system toaccurately locate the mobile user equipment.

Various user equipment (UE) such as computers (fixed or portable),mobile telephones, personal data assistants or organisers and so on areknown to the skilled person and these can be used to communicate withother user equipment in a communication system or to access the Internetto obtain services. Mobile user equipment is often referred to as amobile station (MS) and can be defined as a means which is capable ofcommunication via a wireless interface with a another device such as abase station of a mobile telecommunication network or any other station.Such a mobile user equipment can be adapted for voice, text message ordata communication via the wireless interface.

It is well known by the skilled person that it is useful to identify thelocation of UE. Currently there are many methods via which thegeographical location of the UE can be established. Each of thesemethods has advantages and disadvantages in relation to one another. Forexample some methods calculate the UE location precisely but take a longtime to do so. Other methods are quicker but are less accurate orrequire more processing power. Many of these location estimatingmechanisms are known to be useable with location services (LCS) incommunication systems. Some of these are the time of arrival (TOA),enhanced observed time difference (E-OTD), observed time difference ofarrival (OTDOA), global positioning system (GPS positioning mechanism),timing advance (TA), strength of signals received by the MS from servingand neighbour cells (RXLEV's)

Through use of at least one of these methods the LCS provides means tolocate a UE. The public land mobile network (PLMN) can thus provide alocation application with a geographical location of the UE. Thelocation application which uses this information may reside within thePLMN (in either the UE or in the network itself) or outside the PLMN (inan external application). Positioning may be initiated either by thenetwork, the UE or an external application. The various positioncalculating mechanisms measure various system parameters including powerand propagation delays of signals received at the UE.

Because of the intrinsic nature of electromagnetic waves propagation,when a signal propagates through a certain path, its intensity decreasesand its propagation time increases with the distance between transmitterand receiver. This effect occurs in mobile communication systems as wellas in general. The attenuation experienced by signals transmitted byBase Transceiver Stations (BTSs) and received by mobile UE such asMobile Stations (MSs) is one of the reasons why, in order to guaranteeat the MS side a signal of reliable quality, the service area is coveredby installing many BTSs.

Often there is a need to extend the coverage area of a certain cell. Itis then possible to connect a repeater to a BTS (which is then termedthe donor BTS). The connection between donor BTS and repeater can beimplemented through air, optical fibre or any other physical connection.The repeater is installed at a certain distance from the donor BTS (forexample at the edge of the cell, where the strength of signals isapproximately at the MS sensitivity level) and its basic function is toreceive the signal transmitted by the donor BTS, regenerate it (i.e.amplify it) and re-transmit it. Furthermore, the repeater, due to itsinternal configuration, introduces an additional delay to the signalreceived from the donor BTS and retransmnitted. Repeaters can also beused instead of BTS's in order to reduce costs.

When a MS receives a signal directly from a certain serving BTS, as thepropagation delay increases, the signal's intensity decays. In thissense, propagation delay and intensity of the received signal are bothconsistent measures of the propagation path's length. On the other hand,the signal received by a MS from a repeater has an intensity higher thanthe intensity of the same signal if the MS received it directly from thedonor BTS. Additionally, due to the repeater's internal delay, thepropagation delay of the signal received by the MS is larger than thedelay that would affect the same signal, if it was received directlyfrom the serving BTS. The consistency between propagation delay andstrength of the signal ceases to exist when the signal is receivedthrough a repeater. In fact, there will be an increase of propagationdelay (due to the repeater's internal delay) whilst the strength of thereceived signal is regenerated (increased) by the repeater's amplifier.

The effect of a repeater on propagation delay and signal strength isthus such that as the MS moves further away from the BTS within the BTScoverage area, the average propagation delay increases and the averagestrength of the signal received from the serving BTS decays. At theborder of the BTS coverage area, the signal strength is very low and, ifa repeater was not present, the connection should soon be handed over toa new serving cell. When the MS crosses the border between BTS coveragearea and repeater coverage area, the signal level increases, thanks tothe repeater's amplifier, to levels needed for reliable communications.At the same time, the propagation delay affecting the signal received bythe MS increases, due to the repeater's internal delay. When the MSmoves further away from the repeater, propagation delay and signalstrength behave as in the BTS coverage area but, in absolute terms, theyare not anymore representative of the length of the propagation pathbetween donor BTS and MS.

From a communication system operator's point of view, repeaters offer acost effective solution to many coverage problems. However, repeatersaffect negatively other applications such as the LCS application in acommunication system. This is because as noted above in LCSapplications, the unknown location of a MS is calculated by processingmeasurements performed on the radio signals exchanged between MS andsurrounding BTSs or BTSs and other network elements (LocationMeasurements Units, (LMU) for example). There are many such knownposition calculating mechanisms and more are being continuallydeveloped. The measurements performed on radio signals includeintrinsically the information of where the MS is located with respect toother network elements involved in the measurement process. For example,TA is an estimate of the absolute propagation delay (or equivalently,the absolute distance) between the MS to be located and the serving BTS;RXLEVs can be used to determine the absolute distance (and possibly theorientation) of the MS from the BTSs from which RXLEVs are measured;GTDs measure the relative distance (i.e., difference in absolutedistances) between the MS and a pair of BTSs (the serving and oneneighbour).

To allow location calculation algorithms to estimate the unknown MScoordinates from a set of measurements (TA, RXLEVs, GTDs etc.) thecoordinates of the BTSs involved in the measurement process must beknown. The coordinates are obtained by matching BTS identificationparameters such as BSIC (Base Station Identity Code), CI (CellIdentity), as well as ARFCN (Absolute Radio Frequency Channel Number),available over the radio interface, with the equivalent parametersstored in an LCS database, and retrieving the corresponding BTScoordinates from the database. If such coordinates are wrong, the MSlocation estimate is wrong. This happens when, for example, the BTScoordinates in the LCS database are wrong.

The MS location estimate is also wrong when BTS coordinates in the LCSdatabase are correct but the MS performs measurements through arepeater. In fact, BSIC, CI and often ARFCNs are completely transparentto a repeater. As a result, when a MS performs measurements on thesignal received through a repeater, it identifies correctly the donorBTS but the measurements, due to the additional delay and amplificationintroduced by the repeater, are not consistent with the location of thedonor BTS retrieved from the LCS database. This results in wronglocation estimates.

The negative effects of repeaters on Uplink TOA (Time of Arrival), E-OTD(Enhanced Observed Time Difference) and RIT (Radio Interfaced Timing)measurements, needed for LCS, are mentioned in GSM standards, see forexample ETSI, Technical Report “Digital cellular telecommunicationssystem (Phase 2+); Radio network planning aspects (GSM 03.30 version8.3.0 Release 1999),” doc. ESTI TR 101 362 V8.3.0 (2000-04). One of thesolutions to the problem proposed therein is to reject all themeasurements when there is a possibility that they are performed onsignals received through a repeater. However this is only possible whenthe MS measures enough BTSs. Moreover in the case of E-OTD, for example,if the repeater is connected to the serving BTS, it affects all themeasurements; thus all E-OTD measurements need to be rejected.

Another possibility which has been considered is to reject themeasurements only if they are affected by a repeater or, eventually,correct them by compensating the repeater's effects. However in both ofthese cases, it is necessary to determine whether the signal used toperform measurements is being received by the MS directly from the donorBTS or through a repeater. This has proved to be problematical.

It is an aim of embodiments of the present invention to at least partlymitigate the above mentioned problems.

According to a first aspect of the present invention there is provided amethod for determining if a signal received at a radio receiver in acommunication system is transmitted to the receiver via a direct radiolink comprising the steps of: determining a signal characteristic basedon one or more signal measurements collected at the receiver; comparingthe signal characteristic as determined with at least one predeterminedsystem parameter; and responsive to said comparison determining if saidsignal is received via a direct link.

According to a second aspect of the present invention there is provideda method for determining if a signal received at a radio receiver in acommunication system is transmitted to the receiver via a direct radiolink comprising the steps of: determining at least two different typesof signal characteristics based on one or more signal measurementreceived by the receiver; comparing the determined different types ofsignal characteristics; and responsive to said comparison determining ifsaid signal is received via a direct link.

According to a third aspect of the present invention there is provided amethod for determining if a signal received at a mobile user equipmentin a communication system is transmitted to the user equipment via adirect link comprising the steps of: receiving a plurality of signalcharacteristic measurements each indicating a characteristic of arespective signal received by the user equipment; determining a firstvalue representing the mean of a first characteristic indicated by saidplurality of measurements; determining a difference between said firstvalue and a second value representing at least one predetermined systemparameter; and responsive to said difference determining if said signalis received via a direct link.

According to a fourth aspect of the present invention there is providedapparatus, arranged to determine if a signal received at a radioreceiver in a communication system is transmitted to the receiver via adirect radio link, comprising; means to determine a signalcharacteristic based on one or signal measurements collected at thereceiver; and comparison means for comparing the signal characteristicwith at least one predetermined system parameter; whereby said signal isdetermined to be received via a direct link in response to saidcomparisons.

According to a fifth aspect of the present invention there is providedapparatus, arranged to determine if a signal received at a mobile userequipment in a communication system is transmitted to the user equipmentvia a direct link, comprising; means for receiving a plurality of signalcharacteristic measurements each indicating a characteristic of arespect signal received by the user equipment; means for determining afirst value representing the mean of a first characteristic indicated bysaid plurality of measurements; means for determining a differencebetween said first value and a second value representing at least onepredetermined system parameter; and means responsive to said differencefor determining if said signal is received via a direct link.

Embodiments of the present invention provide the advantage that when arepeater is connected to a certain BTS it is possible to determine incertain conditions whether the signal received by a certain MS is comingdirectly from the serving BTS or through the repeater. This is done byanalyzing the consistency between propagation delay and intensity of thesignal received by the MS.

According to certain embodiments a set of propagation delay and power ofreceived signal observations are collected. These sets of measurementsare used to calculate an estimate of the average propagation delayand/or average received power. By combining the estimated averagepropagation delay and average received power, a decision can be taken onwhether the signal on which the measurements have been performed isreceived by the MS directly from the donor BTS or not. The decision istaken by exploiting the discontinuity generated by the repeater and theconsequent lack of consistency between propagation delay and receivedstrength of the signal received through a repeater. The method may beimplemented by using classical hypothesis testing techniques.

A statistical approach, such as the one proposed herein is advantageousbecause it takes into account the random fluctuations affecting ingeneral the radio wave propagation over the mobile channels and inparticular the propagation delay and received power observations used todetect the presence of a repeater. In general, the larger the set ofobservations is, the more reliable the detection process outcome is.

Embodiments of the present invention also have the advantage that theyrely only on propagation delay and signal strength measurements. Suchmeasurements have been made available in the GSM standards to ensurereliable and efficient communications. In GSM, the parameter TimingAdvance (TA) is defined to compensate the propagation delay effects onthe TDMA access scheme. The TA is an estimate of the round trip MS toserving BTS propagation delay. It is used to compensate the effect ofdifferent propagation delays affecting bursts transmitted by differentmobiles located at different distances from the same serving BTS.Moreover, to ensure the continuity of communications, even thoughterminals are moving and the cell coverage is spatially limited,handover mechanisms are introduced. In GSM, the handover is performedalso by taking into account the strength of the signal received by a MSfrom the serving BTS (Received Level—RXLEV).

Embodiments of the present invention will now be described hereinafter,by way of example only, with reference to the accompanying drawings inwhich:

FIG. 1 illustrates a general LCS logical architecture;

FIG. 2 illustrates the propagation delay and power attenuation ofsignals received by a MS;

FIG. 3 illustrates a direct link and an indirect link;

FIGS. 3 a and 3 b illustrates probability distribution functions;

FIG. 4 illustrates how a choice of equations is made;

FIG. 5 illustrates a mobile user equipment; and

FIG. 6 illustrates a multi-repeater system.

In the drawings like reference numerals refer to like parts.

Location services (LCS) are logically implemented on the GSM/UMTS(Global System for Mobile communications/Universal MobileTelecommunications System) structure by the addition of a certain numberof network elements. These are the serving mobile location centre(SMLC), the gateway mobile location centre (GMLC), and locationmeasurement units (LMU)'s. A general LCS logical architecture isillustrated in FIG. 1. It will be understood that embodiments of thepresent invention can be applied to other communication systems.

A mobile station (MS) 100 can be a mobile telephone or a laptop computerwhich has a radio modem or a fax adapted for radio access. The term MSis used here as an example of mobile user equipment (UE). Thiscommunicates with the base transceiver station (BTS) 101 over the radiointerface (U_(M) Interface). The term BTS is used here also to cover theUMTS terrestrial radio access network (UTRAN) corresponding to thenetwork element node B. The BTS is equipment for transmission andreception of signals and may additionally include ciphering equipment.In addition to the BTS 101 the MS 100 can communicate with repeaterstations 130 (one shown). These are placed in the communication systemby network operators to boost signals from the BTS. They communicatewith the MS 100 and/or BTS 101 via the U_(m) interface. The BTS in turncommunicates with a base station controller (BSC) 102 via link 103(A-Bis in GMS, Iub in UMTS). The term BSC is used here also to cover theUTRAN corresponding network element which is the radio networkcontroller (RNC). The BSC sets up the radio channels for signalling andtraffic to the core-network (CN) node 104 via link 105. This forms partof the core-network 125.

The CN node can be either a mobile switching centre (MSC) or servingGPRS support node (SGSN) depending on the switching domain (circuitswitched or packet switched). The CN node 104 is a switching node havingmany functions. In particular, the CN node performs connectionmanagement, mobility management and authentication activities. In thisexample the CN node also contains the cell control function and serviceswitching functions defined by the IN/CAMEL (IntelligentNetwork/Customized Applications for Mobile network Enhanced Logic)architecture. However, in the package switched domain thesebefore-mentioned CN node functions may be split to separate networkelements. Each CN node can control a number of BSC which are referred toas being in an CN node service area. In general BTSs and BSCs togetherform the radio access network (RAN) 126, which is referred to as thebase station sub-system (BSS) in GMS and UTRAN in UMTS.

The CN node 104 is connected to the gateway mobile location centre(GMLC) 106 via the L_(g) interface 107 which contains functionalityrequired to support LCS. In one PLMN there may be more than one GMLC.The GMLC is the first node an external LCS client accesses in GSM PLMN.

An LCS client 109 is a logical functional entity that requires, from theLCS server function in the PLMN, location information for one or moretarget MS with a specified set of parameters such as quality of service(QoS). The LCS client may reside in an entity (including for example theMS), within the PLMN or in an entity external to the PLMN. An externalLCS client 109 is shown by way of example only in FIG. 1 whichcommunicates with the GMLC 106 via the L_(e) interface 110.

In response to a location request from an LCS client, the GMLC mayrequest routing information from the home location register (HLR) 111 ofthe system via the L_(h) interface 112. The HLR is a database whichallows a mobile subscriber to be permanently registered in the system.The HLR keeps track continuously of the location of a subscriber or MSi.e. via the Visitor Location Register (VLR) or SGSN. In addition to theHLR, each CN node 104 is associated with a database containing detailsof subscribers temporarily in the service area of that CN node. Incircuit switched domain this database is called Visitor LocationRegister (VLR), and in the packet switched domain the database iscontained in the SGSN.

After performing registration authorisation the GMLC 106 sendspositioning requests to and receives final location estimates from, theCN node in the service area in which the MS is currently located (orvisiting).

The serving mobile location centre (SMLC) 113 contains functionalityrequired to support LCS. In one PLMN there may be more than one SMLC113. The SMLC 113 manages the overall coordination and scheduling ofresources required to perform positioning of a mobile station. It alsocalculates the final location estimate and accuracy.

Two types of SMLC are possible. These are the Core Network (CN) basedSMLC, which supports the L_(s) interface 116 which is the interfacebetween the SMLC and CN node, and the Radio Access Network (RAN) basedSMLC which supports the L_(b) interface 117 between the SMLC 113 and theBSC 102. A CN based SMLC supports the positioning of a target MS viasignalling on the L_(s) interface to the visited CN node. A RAN basedSMLC supports positioning via signalling onto the L_(b) interface. InUMTS, SMLC functionality is contained in the BSC 102, i.e. Radio NetworkController (RNC).

The SMLC can control a number of location measurement units (LMU)'s forthe purpose of obtaining radio interface measurements to locate or helplocate MS subscribers in the area that it serves.

In order to provide location information about the MS 100, the MS may beinvolved in various positioning procedures. It may also calculate itsown location estimate and accuracy by means of various MS based positioncalculating methods. These position calculating methods are well knownand will not be described in detail hereinafter for the sake of brevity.Alternatively the position of the MS may be calculated in some otherpart of the communication system.

The LMU (shown in FIG. 1) may make radio measurements to support one ormore of these positioning measurements. Two types of LMU are defined.Type A LMU 118 which is accessed over the air interface (U_(m)) and typeB LMU 119 which is accessed over the interface 120 to the BSC 102.

A type A LMU is accessed exclusively over the GSM air interface (U_(m))interface. There is no wired connection to any other network element. Atype A LMU has a serving BTS and BSC that provides signalling access toa controlling SMLC. With a CN based SMLC a type A LMU has a serving CNnode.

A type B LMU is accessed over the interface 120 from a BSC. The LMU maybe either a stand-alone network element addressed using some pseudo-cellID or connected to, or integrated in, a BTS. Signalling to a type B LMUis by means of messages routed through the controlling BSC for a BSSbased SMLC or messages routed through a controlling BSC and CN for a CNbased SMLC.

FIG. 2 illustrates how the propagation delay (τ) and power (P_(R)) ofsignals received at the MS 100 vary as the distance (d) of the MS 100from the BTS changes. As illustrated the propagation delay shown bycurve 200 steadily increases as the distance from the BTS increases. Thepower of the received signal 201 steadily decreases due to attenuationeffects as the signal propagates. Both signals are susceptible to randomfluctuations resulting in a band of possible values centred around thetwo curves 200, 201. These bands are shown as 202, 203 showing thepossible range of values, at any distance, for the delay and powersignals respectively.

A repeater 130 is placed a distance d_(c) away from the BTS 101. Thismay represent a distance at which the signals are becoming so weak thata handover would be likely. This handover zone is illustrated by theshaded region 205 bounded by distances d_(A) and d_(B). Alternatively arepeater may be placed at any point where a system operator constructinga communication system may feel it is advisable. The repeater increasesthe coverage area of the BTS.

Curve 206 illustrates the propagation delay of the signals received by aMS a distance greater than d_(c) from the donor BTS 101. Curve 207illustrates the power of the received signal in that region. It will benoted that a discontinuity (or step) takes place in the curves 200, 206which is due to the internal delay in the repeater. Likewise adiscontinuity (or step) takes place in the curves 201, 207 which is dueto the power amplification of the repeater which regenerates the powerof the received signals. The gain of the repeater may be set tocompensate for the attenuation effects.

FIG. 3 illustrates the power loss and propagation delays in the system.To simplify the example, two terminals, MS0 300 and MS1 301, areconsidered. It will be understood that the present invention isapplicable to use with one or more MS in general. The first mobilestation 300 communicates directly with the serving BTS (via a directlink), the second mobile station 301 communicates with the serving BTSthrough the repeater 130 (via an indirect link). Given the followingdefinitions:

-   -   For the Direct Link (BTS-MS0)        -   P_(T,B): is the power of the signal transmitted by the            serving BTS at the BTS's antenna input, measured in dBm;        -   τ_(B,0): is the propagation delay on the direct link,            measured in seconds.        -   L_(B,0): is the attenuation on the direct link including the            BTS's anntena gain and path-loss, measured in dB;        -   P_(R,0): is the power of the signal received by the MS on            the direct link, measured in dBm;    -   For the Indirect Link (BTS-Repeater-MS1)        -   P_(T,D): is the power of the signal transmitted by the            serving BTS at the BTS's donor antenna input on the link            BTS-Repeater, measured in dBm;        -   τ_(B,R): is the propagation delay on the link BTS-Repeater,            measured in seconds;        -   L_(B,R): is the attenuation on the link BTS-Repeater,            including the BTS's donor antenna gain, the Repeater's donor            antenna gain and the path-loss, measured in dB;        -   P_(R,R): is the power of the signal received by the Repeater            on the link BTS-Repeater at the output of the Repeater's            donor antenna, measured in dBm;        -   τ_(R): is the Repeater's internal delay, measured in            seconds;        -   G_(R): is the gain of the Repeater's amplifier, measured in            dB:        -   P_(T,R): is the power of the signal transmitted by the            Repeater at the Repeater's antenna input, measured in dBm;        -   τ_(R,1): is the propagation delay on the Repeater-MS1 link,            measured in seconds;        -   L_(R,1): is the attenuation on the Repeater-MS1 link            including the Repeater's antenna gain and path-loss,            measured in dB;        -   P_(R,1): is the power of the signal received by the MS on            the indirect link, measured in dBm;

Using this terminology, the power of the signal received by MS0 on thedirect link can be expressed as follows:P _(R,0) =P _(T,B) −L _(B,0)   (1)

The propagation delay of the signal on the direct link is given by:τ_(BTS→MS0)=τ_(B,0)   (2)

The equation describing the power of the signal received by MS1 on theindirect link is:P _(R,1) =P _(T,B) −L _(B,R) +G _(R) −L _(R,1)   (3)

The propagation delay affecting the signal on the same link is given by:τ_(BTS→MS1)=τ_(B,R)+τ_(R)+τ_(R,1)   (4)

The path-loss of the radio signal propagating from BTS to MS0 on thedirect link can be expressed as a function of the distance between theBTS antenna and the MS0 antenna, d_(B,0), for example by means of alog-distance path-loss formula as described in Y. Okumura et al., “FieldStrength and Its Variability in UHF and VHF Land-mobile Radio Service.”Rev. Elec. Commun. Lab., vol. 16, 1968 and M. Hata, “Empirical Formulafor Propagation Loss in Land Mobile Radio Services,” IEEE Transactionson Vehicular Technology, vol. VT-29, no. 3, pp. 317-325, August 1980.The path-loss formula is:L _(B,0) =A _(B,0) +n _(B,O)log₁₀ d _(B,0)   (5)Where A_(B,0) is the attenuation at a close-in distance from the BTSantenna and n_(B,0) is the propagation factor. By expressing d_(B,0) asproduct of the propagation delay over the direct link, τ_(B,0), and thespeed of propagation of the radio waves on the direct link, c₀, thereceived power P_(R,0) in equation (1) and the propagation delayτ_(BTS→MS0) in equation (2) can be connected as follows:

$\begin{matrix}\left\{ \begin{matrix}{P_{R,0} = {P_{T,B} - \left\lbrack {A_{B,0} + {n_{B,0}{\log_{10}\left( {c_{0}\tau_{B,0}} \right)}}} \right\rbrack}} \\{\tau_{{BTS}\rightarrow{MSO}} = \tau_{B,O}}\end{matrix} \right. & (6)\end{matrix}$

With analogous definitions, a similar connection can be found betweenthe power of the signal received by the MS through the indirect link,P_(R,!), and the propagation delay affecting the signal on the samelink, τ_(BTS→MS!):

$\begin{matrix}\left\{ \begin{matrix}{P_{R,1} = {P_{T,D} - L_{B,R} + G_{R} - \left\lbrack {A_{B,1} + {n_{B,1}{\log_{10}\left( {c_{1}\tau_{B,1}} \right)}}} \right\rbrack}} \\{\tau_{{BTS}\rightarrow{MS1}} = {\tau_{B,R} + \tau_{R} + \tau_{R,1}}}\end{matrix} \right. & (7)\end{matrix}$

To take into account the uncertainties in the log-distance path-lossmodels used on the direct link and on the Repeater-MS1 link over theindirect link, two additive random variables, u₀ and u_(i), can be addedto the expressions of the received powers P_(R,0) and P_(R 1).Analogously, two additive random variables, ε₀ and ε₁, can be added tothe expressions of the propagation delays τ_(BTS→MS0) and τ_(BTS→MS1)account for the effect of the impairments over the direct link and overthe Repeater-MS1 link on the estimation of the propagation delays.

An additional term, δ_(R), can likewise be introduced in the expressionof τ_(bTS→MS1) to take into account the variations of the repeater'sinternal delay (due to random variations and variations dependent on theradio signal frequency).

The addition of the uncertainty terms defined above to equations (6) and(7) leads to the following sets of equations:

$\begin{matrix}\left\{ \begin{matrix}{P_{R,0} = {P_{T,B} - \left\lbrack {A_{B,0} + {n_{B,0}{\log_{10}\left( {c_{O}\tau_{B,0}} \right)}}} \right\rbrack + u_{0}}} \\{\tau_{{BTS}\rightarrow{MS0}} = {\tau_{B,0} + ɛ_{0}}}\end{matrix} \right. & (8) \\\left\{ \begin{matrix}{P_{R,1} = {P_{T,D} - L_{B,R} + G_{R} - \left\lbrack {A_{R,1} + {n_{R,1}{\log_{10}\left( {c_{1}\tau_{R,1}} \right)}}} \right\rbrack + u_{1}}} \\{\tau_{{BTS}\rightarrow{MS1}} = {\tau_{B,R} + \tau_{R} + \tau_{R,1} + ɛ_{1} + \delta_{R}}}\end{matrix} \right. & (9)\end{matrix}$

Referring to equations (8) and (9) one can assume, for simplicity, thatthe system is ideal (in which case u₀=0, u_(i)=0, and δ_(R)=0) and“completely balanced”, meaning that the BTS transmission power on thedirect link and on the link with the Repeater's donor antenna is thesame (P_(T,B=P) _(T,D)). This is the case when the Repeater amplifiesthe signal received directly from the BTS antenna (i.e. the BTS antennaand the BTS donor antenna are the same antenna). Alternatively a BTS mayinclude more than one antenna in which case to be ‘completely balanced’the emitted power on the antennas should match. The attenuation on theradio path between the BTS's antenna and MS0 is the same as theattenuation on the radio path between Repeater's donor antenna and MS1(L_(B,0)=L_(R,1)). The propagation factor and speed on both direct andindirect links are the same (n_(B,0)=n_(B,1) and c₀=c₁). Moreover, ifthe distance between the mobile terminals and the antennas from whichthey are receiving their signals is the same (d_(B,0)=d_(R,1)), thepower received by MS1 call be expressed asP_(R,1)=P_(R,0)−L_(B,R)+G_(R). If the Repeater's internal gain is chosenin such a way to compensate exactly the attenuation over theBTS-Repeater link (L_(B,R)=G_(R)) the power of the signal received byMS0 and MS1 is exactly the same: P_(R,1)=P_(R,0).

In these particular conditions, the power of received signals alone doesnot allow one to identify which terminal is connected with the BTSthrough a direct link and which through a repeater. In order to separatedirect and indirect connections (communications links) an analysis ofthe propagation delays should be included. In fact, most likely thepropagation delay affecting the signal received by MS1 is larger thanthe one affecting MS0 In ideal conditions, where there is an absence ofuncertainty in propagation delay estimation (ε₀=ε₁=δ_(R)=0), thepropagation delay affecting the signal received by MS1 is τ_(BTS→MS1)τ_(BTS→MS0) +τ_(B,R) +τ_(R), larger than the propagation delay affectingthe signal received by MS0 τ_(BTS→MS0) (in fact, τ_(B,R) τ_(R)≧0). Thiscondition allows one to determine that MS0 is connected to the BTSthrough a direct link and MS1 through an indirect link.

In a non ideal system (u₀, u₁, ε₀, ε₁, δ_(R) are non zero), the basicreasonings explained above still hold. However, each single propagationdelay and signal power observation is subject to random fluctuations(see FIG. 2). Thus the joint comparison between the pairs (P_(R,1),P_(R,0)) and (τ_(BTS→MS1), τ_(BTS→MS0)) may fail to determine whichterminal is connected to the Repeater. The size of random fluctuationsdepends on the propagation environment, characteristics of the hardwareused, and properties of the measurement methods used to determine thepropagation delay and signal power observations. The dispersion ofrandom fluctuations can be reduced by averaging multiple sets ofobservation pairs. Thus as the number of samples increases, the varianceof the sample mean estimation decreases.

Equations (8) and (9) can be manipulated to obtain the followingexpressions for the propagation delays affecting the signals received byMS0 and MS1:

$\begin{matrix}\left\{ \begin{matrix}{\left. {BTS}\rightarrow{MSO} \right. = {{\frac{1}{c_{0}}10^{\frac{P_{T,B} - P_{R,0} - A_{B,O} + n_{0}}{n_{B,0}}}} + 0}} \\{{\left. {BTS}\rightarrow{MS1} \right. = B},{R + R + {\frac{1}{c_{1}}10^{\frac{P_{T,D} - P_{R,1} - L_{B,R} + G_{R} - A_{R,1} + n_{1}}{n_{R,1}}}} + \; 1 + 1}}\end{matrix} \right. & (10)\end{matrix}$

Analogously, the following dual expressions for the power of the signalsreceived by MS0 and MS1 can be obtained:

$\begin{matrix}{\quad\left\{ \begin{matrix}{P_{R,0} = {P_{T,B} - \left\{ {A_{B,0} + {n_{B,0}{\log_{10}\left\lbrack {c_{0}\left( {\tau_{{BTS}\rightarrow{MS0}} - ɛ_{0}} \right)} \right\rbrack}}} \right\} + u_{0}}} \\{P_{R,1} = {P_{T,D} - L_{B,R} + G_{R} - \left\{ {A_{R,1} + {n_{R,1}{\log_{10}\left\lbrack {c_{1}\left( {\tau_{{BTS}\rightarrow{MS1}} - \tau_{B,R} -} \right.} \right.}}} \right.}} \\{\left. \left. \left. \mspace{515mu}{\tau_{R} - ɛ_{1} - \delta_{R}} \right) \right\rbrack \right\} + u_{1}}\end{matrix} \right.} & (11)\end{matrix}$

Equations 10 and 11 relate the propagation delay to the measured powerof the received signals. In equation 10 the delay via a direct(τ_(BTS→MS0)) or indirect (τ_(BTS→MS1)) communication link are expressedin terms of the corresponding measured power levels (P_(R,0) and P_(R,1)respectively). In equation 11 the power levels P_(R,0), P_(R,1) receivedat the MS 300 and 301 respectively are defined in terms of the measuredpropagation delays. From these two equations it is possible to definetwo formulations answering the question of whether the signal receivedby the MS100 propagates through a direct link or indirect link (i.e. viaa repeater station 130). These two alternative formulations are:

Formulation A. Given a set of observations of propagation delay {τ₁, . .. , τ_(n)} and corresponding signal power {P_(R,1), . . . , P_(R,n)},performed on the signals received by a certain MS, decide whether asignal received by the MS is propagating through a direct link.

Formulation B. Given a set of observations of propagation delay {τ₁, . .. , τ_(n)} and corresponding signal power {P_(R,1), . . . P_(R,n)},performed on the signals received by a certain MS, decide whether asignal received by the MS is propagating through an indirect link.

The solution of the problems stated as above can be found by usingHypothesis Testing techniques which are well known in the art ofstatistical analysis. In order to apply such techniques the observationsneed in be characterized statistically. This can be done by using eitherof the set of equations 10 or the set of equations 11. The informationcarried by each of the two sets is similar but, for practical reasons,it might be easier to apply the test directly to delay measurements andtake implicitly into account the signal power observations, or viceversa. This will depend on the applications, what measurements areavailable, how they behave statistically, whether analytical expressionsor experimentally measured values for the quantities of interest areused, etc.). Furthermore, depending on the application, eitherFormulation A or Formulation B can be used.

By way of example only the following embodiments are described inrespect of the following assumptions.

-   1. The test is performed according to Formulation A. In other words,    the test uses a set of observations to decide with a certain degree    of confidence if the MS is receiving the signal from the direct    link.-   2. The test is performed using the propagation delay measurements as    reference observations, taking implicitly into account the signal    power observations. In other words, only the set of equations 10 is    used.-   3. The test is performed by applying techniques of hypothesis    testing to the mean value of a set of propagation delay    observations. The details of this technique are described    hereinafter.-   4. Referring to the basic scheme in FIG. 3, the following parameters    of direct and indirect link are assumed to be available that is to    say can be measured or are already known:    -   Direct Link: P_(T,B), A_(B,0), n_(B,0), c₀    -   Indirect Link: P_(T,D), τ_(B,R), L_(B,R), G_(R), τ_(R), L_(R,1),        n_(B,1), c₁

It will be understood that a test according to Formulation B could beused using either of the sets of equations 10 or 11. LikewiseFormulation A could be used but using the set of equations 11 instead of10.

It is now convenient to introduce a discussion of hypothesis testingwhich can be applied to the above described problems. Hypothesis testingis a well known type of inferential statistical process. Hypothesistesting techniques can be used to establish whether results observedfrom an experiment are consistent with a certain understanding(hypothesis) of the underlying physical phenomena. This is achieved byfirst determining the value for certain statistical properties (e.g.,mean value, standard deviation, etc.) of the experiment results that areexpected under the assumption that the hypothesis on the underlyingphysical phenomena is valid. Such expected statistical properties aretypically determined before the experiment is performed. When theexperiment results are available the analogous statistical properties(e.g., mean value, standard deviation, etc.) are calculated for themeasured experimental results. By properly comparing the expected andmeasured statistical properties of the experiment results it is thenpossible to decide whether the underlying hypothesis on the physicalphenomena is correct with a given degree of confidence.

In the present case embodiments of the present invention comprisecollecting a certain set of propagation delays and corresponding signalpower levels measured by the MS 100 on its link with the serving BTS.The hypothesis under test is whether the MS 100 is connected with theserving BTS through a direct link (Formulation A). The hypothesistesting for the mean value is considered here. The procedure consists incomparing the average values (mean values) of the propagation delays andpower levels observed by the MS 100 with the corresponding quantitiesthat are expected to be measured by the MS 100 if it was connected withthe serving BTS through a direct link.

If the observed values differ from the expected mean values by an amountwhich could be statistically expected (i.e., owing to the randomfluctuations of the measurements performed over the direct link) thenone can assume that the MS 100 is connected to the serving BTS through adirect link.

If the observed values differ from the expected mean values by an amountwhich is greater than an amount that could be reasonably determined byrandom measurement fluctuations then the hypothesis that the MS 100 isconnected to the serving BTS through a direct link cannot be accepted.In this case to determine if the MS 100 is connected to the serving BTSthrough an indirect link, the same set of propagation delay and signalpower observations should be tested against the hypothesis that the MS100 is connected to the serving BTS through an indirect link (i.e., byusing Formulation B). A brief discussion of Hypothesis testing for theman value follows but for a fuller understanding reference may be madeto A. Papoulis, Probability, Random Variables, and StochasticProcesses—3rd Ed., McGraw-Hill, 1991.

By way of example consider that the probability density function (PDF)of a random variable (RV) X is a known function ƒx (x,θ) depending on aparameter θ. The goal of hypothesis testing is to collect a set ofobservations of the RV X and, on the basis of such observation, test theassumption θ=θ₀ against the assumption θ≠θ₀. Usually the firstassumption is denoted as the null hypothesis and the second assumptionis denoted as the alternative hypothesis:

$\quad\left\{ \begin{matrix}{{H_{0}\text{:}\mspace{14mu}\theta} = \theta_{0}} & \left( {{null}\mspace{14mu}{hypothesis}} \right) \\{{H_{1}\text{:}\mspace{14mu}\theta} \neq \theta_{0}} & \left( {{alternative}\mspace{14mu}{hypothesis}} \right)\end{matrix} \right.$

The null and alternative hypothesis are mutually exclusive and areexhaustive. They cannot occur at the same time and no other outcomes arepossible.

Generally speaking X is the outcome of a certain experiment. To decidewhether the null hypothesis should be accepted or rejected, theexperiment is repeated n times and the observed outcomes are collected.The resulting set (or sample) of outcomes {x₁, . . . x_(n)} is aspecific observation of the sample {X₁, . . . X_(n)} made of n randomvariables (e.g. X_(i) is the random variable “outcome of the i^(th)trial” and x_(i) is a realization of the random variable X_(i)). Thedecision on whether the null hypothesis should be accepted or rejectedis based on experimental evidence. If the sample vector {X₁, . . . ,X_(n)} has a PDF ƒ(X₁, . . . X_(n); θ₀) which is negligible in a certainregion D_(c) (the critical region) of the sample space, takingsignificative value in the complement region D_(c), then H₀ will beaccepted only if the observed sample will fall in D _(c); otherwise H₀will be rejected. In hypothesis testing, two types of error are defined:

Type 1 error.

This error occurs when H₀ is true but the experimental evidence resultsin rejection of it. The probability of a Type I error isα=P{{X ₁ , . . . X _(n) }∈D _(c) |H ₀}  (28)

The probability that H₀ is accepted when it is true is thus 1−α.

-   -   Type II error.

This error occurs when H₀ is false but the experimental evidence resultsin the acceptance of it. The probability of a Type II error is ingeneral dependent on θ:β(θ)=P{X ₁ , . . . , X _(n) }∉D _(c) |H ₁}

The probability that H₀ is rejected when it is false is 1−β(θ)=P{{X₁, .. . X_(n)}∉D_(c)| H₁} This is the power of the test. The critical regionD_(c) must be chosen to keep both α and β(θ) low, however, when αincreases β(θ) decreases and vice versa.

In the case of Hypothesis testing for the mean, θ is the mean value ofthe random variable X and θ₀ is the mean value of the random variable Xif the null hypothesis H₀ holds. Hypothesis testing for the mean usessamples to draw inferences about the mean value of the population. A setof samples is drawn from the population and the average value of suchset of samples (sample mean) is compared to the mean of the populationunder null hypothesis. To make the decision clear cut the samplingdistribution is divided into two regions:

-   -   Outcomes likely to occur if H₀ were true. This occurs when the        sample mean has a value close to the mean value of the        population under hypothesis H₀ (referred to also as “H₀        population mean”). In this case the results are consistent with        H₀. This is also called the region of retention.    -   Outcomes unlikely to occur if H₀ were true. This occurs when the        sample mean has a value far from the H₀ population mean. In this        case the result is not consistent with H₀. This is also called        the region of rejection or critical region D_(c).

The critical region D_(c) is the area of the sampling distribution whichcontains values that would be very unlikely to occur if the H₀ weretrue. In other words, it is very unlikely that a random sample from theH₀ population would result in a sample mean as extreme or more extremethan the one obtained. The critical region is separated from the rest ofthe sampling distribution based on the value selected for α. Thecritical value is the value for the statistic that serves as theboundary between the critical region and the rest of the samplingdistribution.

FIGS. 3 a and 3 b illustrate normal distributions 320, 321 which showhow measured results are spread about a central expected average valueμ₀. The distributions are symmetric with scores more concentrated in themiddle than at the edges (the tails).

The critical regions 322, 323 described hereinabove occurs in thesetails and is selected according to the α level selected. For example inFIG. 3 a the critical regions are shown hashed. These regions representvalues for which it is very unlikely that a random sample from thepopulation would result with.

Hypothesis testing for the mean is usually performed using a “teststatistic”. The test statistics is a RV Q defined as a function of asample vector {X₁, . . . , X₁}:Q=g(X ₁ , . . . , X _(n))  (30)

The transformation g (X₁, . . . , X_(n)) could be used for instance totransform an n-dimensional vector {X₁, . . . , X_(n)} into one singlereal number.

The test statistics Q has a PDF ƒ_(Q)(q,θ). The critical region R_(c) isthe set of the real axis where the PDF of Q under hypothesis H₀ (i.e.,ƒ_(Q)(q,θ₀)) is negligible.

Errors of Type I and Type II have the following probabilities:α=P{{X ₁ , . . . , X _(n) }∈R _(c) |H ₀}=∫_(Rc)ƒ_(Q)(q,θ₀)dqβ(θ)=P{{X ₁ , . . . , X _(n) }∉R _(c) |H ₁}=∫_(Rc)ƒ_(Q)(q,θ)dq

The test is carried out in the following steps:

-   1. Select the test statistics Q-   2. Determine the PDF of Q,ƒ,_(Q)(q,θ)-   3. Observe the sample {X₁, . . . , X_(n)} and compute q=g(X₁, . . .    , X_(n))-   4. Assign a value for α-   5. Determine the critical region R_(c) which ensures that the target    α be achieved, minimizing at the same time the corresponding value    for β(0).-   6. Reject H₀ if q∈R_(c)

In the case of Hypothesis testing for the mean, θ is the mean value ofthe random variable under test X and θ₀ is the mean value of the randomvariable X if the null hypothesis H₀ holds. When this type of test isperformed the null hypothesis assumes that the mean μ of a RV X equals acertain constant μ₀. Alternative hypothesis can be one of the following:

-   -   1. H₁: μ≠μ₀    -   2. H₁: μ>μ₀    -   3. H₁: μ<μ₀

Two cases are considered in the following. In the first one the varianceσ² of X is known, in the second it is unknown and derived from thesample vector. Variance is an indication of how each of the individualvalues in a sample differ from the average calculated from the samples.

Case 1: Known Variance

If the variance of X is known to be a σ², the following test statisticscan be selected:

$\begin{matrix}{Q = \frac{\overset{\_}{X} - \mu_{0}}{\sigma/\sqrt{n}}} & (33)\end{matrix}$Where X is the sample mean defined as:

$\begin{matrix}{\overset{\_}{X} = \frac{\sum\limits_{i = 1}^{n}\; X_{i}}{n}} & (34)\end{matrix}$

X is a function of the RVs {X₁, . . . X_(n)}; and is thus is a randomvariable itself. If {x₁, . . . , x_(n)} are the values of the specificsample extracted, then x given by:

$\begin{matrix}{\overset{\_}{x} = \frac{\sum\limits_{i = 1}^{n}\; x_{i}}{n}} & (35)\end{matrix}$is the average of the specific sample extracted i.e., the specific valueof the RV X. The distribution of X is Gaussian X˜N(μ,σ²/n) (if X has aGaussian distribution) or asymptotically Gaussian (if X does not have aGaussian distribution but the size of the sample is large, for examplen>30). As a consequence, Q is a Gaussian RV Q˜N(μ_(Q),σ²/n) where:

$\begin{matrix}{\mu_{Q} = \frac{\mu - \mu_{0}}{\sigma/\sqrt{n}}} & (36)\end{matrix}$

Under hypothesis H₀ Q is a standardized Gaussian with mean value 0 andstandard deviation 1: (Q! H₀)˜N(0,1). Given an assigned value for α, thehypothesis testing proceeds as described in the remainder of thisparagraph for different choices of H₁.

More particularly it can be assumed that ƒ_(Q)(q,θ)=ƒ_(Q)(q,μ) has onemaximum and that ƒ_(Q)(q,μ) is concentrated on the right hand side ofƒ_(Q)(q,μ₀) if μ>μ₀ and on its left hand side if μ<μ₀.

1. H₁: μ≠μ₀

Since under hypothesis H₀, Q calculated from equation (33) is astandardized Gaussian with mean value 0, the null hypothesis is rejectedif the samples collected during the experiments lead to a value of thetest statistics too large or too small. This rule can be formalized asfollows:

-   -   H₀ is rejected if q<c₁, when μ<μ₀, or if q>c₂, when μ>μ₀

The critical regions is thus R_(c)=(−∞,c₁]U[c₂,÷∞). For convenience αcan be equally distributed over the two semi-axes that deternine R_(c):

${{P\text{\{}Q} < {c_{1}{{{{H_{0}\text{\}}} = \frac{\alpha}{2}};{{P\text{\{}Q} > c_{2}}}}H_{0}\text{\}}}} = {1 - \frac{\alpha}{2}}$Resulting c₁ and c₂ defined as the (α/₂)^(th) and the (1−(α/₂))^(th)percentiles of Q:

$\left\{ \begin{matrix}{c_{1} = q_{\frac{\alpha}{2}}} \\{c_{1} = q_{1 - \frac{\alpha}{2}}}\end{matrix}\quad \right.$

The test can be thus stated as follows:

Accept H₀ if and only if q_(α/2)<q<q_(1−α/2)

where β(μ) has the following generic expression:

${\beta(\mu)} = {\int_{q_{\frac{\alpha}{2}}}^{q_{1 - \frac{\alpha}{2}}}{{f_{Q}\left( {q,\mu} \right)}{\mathbb{d}q}}}$

In conclusion, it is important to point out that q_(α/2) and q_(1−α/2)are percentiles of a standardized Gaussian RV with mean value 0 andstandard deviation 1. Values for these percentiles can be found in anystatistics textbook; some of them are reported in table 1 (forhistorical reasons the percentiles, which have been indicated as q_(u)above, when the RV is a standardized Gaussian RV, are denoted as z_(n)).

TABLE 2 U 0.9 0.925 0.95 0.975 0.99 0.995 0.999 0.9995 z_(i1) 1.2821.440 1.645 1.967 2.326 2.576 3.090 3.291

2. H₁: μ>μ₀

In this case, under hypothesis H₁, the most likely values of Qcalculated from equation (33) are larger than the values of Q underhypothesis H₀ (recall that under hypothesis H₀ Q is a standardizedGaussian with mean value 0 and standard deviation 1). The nullhypothesis should be then rejected if the samples collected during theexperiments generate a test statistic too large:

-   -   H₀ is rejected if q>c        and the critical regions is R_(c)−[c,=+∞). By imposing:        α=P{Q>c|H ₀}=1−P{<c1H ₀}

In this case c turns out to be the (1−α)-^(th) percentile of Q,c=q_(1−α). The test can be thus stated as follows. Accept H₀ if and onlyif q<q_(1−α)

β(μ) has the following generic expression:

β(μ) = ∫_(−∞)^(q_(1 − α))f_(Q)(q, μ)𝕕q

q_(1−α) is the (1−α)-^(th) percentile of a standardized Gaussian RV withmean value 0 and standard deviation 1 (see table 1).

3. H₁: μ<μ₀

Following reasoning analogous to that of the preceding cases, the nullhypothesis should be then rejected if the samples collected during theexperiments generates a test statistic too small:

-   -   H₀ is rejected if q<c        and the critical regions is R_(c)−(−∞,c). By imposing        α=P{Q<c H ₀}        c turns out to be the α-th percentile of Q, c=q_(α). The test        can be thus stated as follows:    -   Accept H₀ if and only if q>q_(α)

β(μ) has the following generic expression:

β(μ) = ∫_(q_(α))^(+∞)f_(Q)(q, μ)𝕕q

In this case q_(β)is the α-^(th) percentile of a standardized GaussianRV with mean value 0 and standard deviation 1 (see table 1).

Case 2: Unknown Variance

If the standard deviation σ of the population, is unknown, the followingnormalized RV can be used as the test statistics:

$\begin{matrix}{Q = \frac{\overset{\_}{X} - \mu_{0}}{S/\sqrt{n - 1}}} & (37) \\{where} & \; \\{S^{2} = \frac{\sum\limits_{i - 1}^{n}\left( {X_{i} - \overset{\_}{X}} \right)^{2}}{n}} & (38)\end{matrix}$

S is the sample variance. Now both X and S² are random variables, beingfunctions of the RVs {X_(!), . . . X_(n)}.

It can be shown from “A. Papoulis, Probability, Random Variables andStochastic Processes—3^(rd) Ed., McGraw-Hill, 1991” that underhypothesis H₀, the RV Q defined in (37) has a t-Student distributionwith n−1 degrees of freedom if the distribution of the population fromwhich the sample of dimension n has been extracted has a Gaussiandistribution or the distribution of the population is not Gaussian butit is bell-shaped as the Gaussian.

The analytical expression of the probability density function of arandom variable l with a t-Student distribution and with n−1 degrees offreedom is:

$\begin{matrix}{{{f_{T}(t)} = {\frac{\Gamma\left( \frac{n + 1}{2} \right)}{\sqrt{n\;\pi}{\Gamma\left( \frac{n}{2} \right)}}\left( {1 + \frac{t^{2}}{n}} \right)^{\frac{n + 1}{2}}\left( {{- \infty} < t < \infty} \right)}};{{E\left\{ T \right\}}\mspace{56mu} = 0};{{E\left\{ T^{2} \right\}} = {\frac{n}{n - 2}\left( {n > 2} \right)}}} & (39)\end{matrix}$

ƒ_(T)(t) is symmetric; thus the p-^(th) and the (1−p)-^(th) percentilesare such that t_(1−p)=−t_(p). Recall that the p-^(th) percentile of therandom variable t is such that P(t≦t_(p))=p and, for symmetricdistributions, P(−t_(p)≦t≦t_(p)))=2p−1.

The same results as those obtained in the case of unknown variance canbe used when the variance σ² is not known, provided that the percentilesused are the ones of a t-Student RV with n−1 degrees of freedom,t_(u)(n−1).

1. H₁: μ≠μ₀

-   -   Accept H₀ if and only if

${t_{\frac{\alpha}{2}}\left( {n - 1} \right)} < q < {t_{1 - \frac{\alpha}{2}}\left( {n - 1} \right)}$

${\beta(\mu)} = {\int_{t_{\frac{\alpha}{2}}{({n - 1})}}^{t_{1 - \frac{\alpha}{2}}{({n - 1})}}{{f_{Q}\left( {q,\mu} \right)}{\mathbb{d}q}}}$2. H₁: μ>μ₀

-   -   Accept H₀ if and only if q<t_(1−α)(n−1)

β(μ) = ∫_(−∞)^(t_(1 − α)(n − 1))f_(Q)(q, μ)𝕕q3. H₁: μ<μ₀

-   -   Accept H₀ if and only if q>t_(α)(n−1)

β(μ) = ∫_(^((n − 1)))^(+∞)f_(Q)(q, μ)𝕕q

Some of these percentiles t_(k)(n) are reported in table 2.

TABLE 2 U 0.9 0.95 0.975 0.99 0.995 n = 1 3.08 6.31 12.7 31.8 63.7 21.89 2.92 4.30 6.97 9.93 3 1.64 2.35 3.18 4.54 5.84 4 1.53 2.13 2.783.75 4.60 5 1.48 2.02 2.57 3.37 4.03 6 1.44 1.94 2.45 3.14 3.71 10 1.371.81 2.23 2.76 3.17 20 1.33 1.73 2.09 2.53 2.85 30 1.31 1.70 2.05 2.462.75

The t-Student distribution is asymptotically Gaussian, in fact for:

${{{for}\mspace{14mu} n} > 30},{{t_{u}(n)} = {z_{u}\sqrt{\frac{n}{n - 2}}}}$

Returning to Formulation A of the problem hereinbefore mentioned thenull hypoythesis H₀ and the alternative hypothesis H₁ are defined asfollows:

$\left\{ \begin{matrix}{{H_{0}:{{MS}\mspace{14mu}{connected}\mspace{14mu}{through}\mspace{14mu}{direct}\mspace{14mu}{link}{\quad\quad}}}\quad} \\{H_{1}:{{MS}\mspace{14mu}{not}\mspace{14mu}{connected}\mspace{14mu}{through}\mspace{14mu}{direct}\mspace{14mu}{link}{\quad{\quad\quad}}}}\end{matrix} \right.$

In order to apply hypothesis testing to observations of the propagationdelay affecting the signal received by the MS (either on the direct oron the indirect link), the propagation delay is modeled as a randomvariable (RV), X (i.e, X=τ_(BTS->MS)). For a given value of receivedpower, P_(R), the RV X is defined as follows by using equation (10):X=D[[÷]]+K(P _(R))·η+v  (13)where D, K, (P_(R)), η, ν have different definitions depending on whichhypothesis holds (see table 3). The physical meaning of each term in(13) is explained below:

D is a constant factor representing the additional delay introduced bythe repeater.

It includes the repeater internal delay (τ_(R)) and the delay introducedby the link between BTS and repeater (τ_(B,R)). By definition, thisadditional delay is non zero only under hypothesis H₁. While τ_(B,R)depends on the particular configuration of the link between donor BTSand Repeater (Distance, if the link is a radio link. Group delay andlength of the cable, if the link is through a cable of optical fibre.etc.). τ_(R) depends on the Repeater's hardware. A commercial repeaterin the 900 Mz bandwidth may typically have group delay τ_(R)<5 μs.

TABLE 3 Under hypothesis H₀ Under hypothesis H₁ D 0 τ_(B,R) + τ_(R)K(P_(R)) $\frac{1}{c_{0}}10^{\frac{P_{T,B} - P_{R} - A_{B,0}}{n_{B,O}}}$$\frac{1}{c_{1}}10^{\frac{P_{T,D} - P_{R} - L_{B,R} + G_{R} - A_{R,0}}{n_{R,1}}}$η $\frac{1}{c_{0}}10^{\frac{u_{0}}{n_{B,0}}}$$\frac{1}{c_{1}}10^{\frac{u_{1}}{n_{R,1}}}$ υ ε₀ ε₁ + δ_(R)

K (P_(R)) is a function of the power received by the MS, P_(R). OnceP_(R) is known from the observations, K (P_(R)) is constant. Physically.K (P_(R)) is a delay equivalent to the attenuation experienced by thereceived signal. The equivalence between attenuation of the receivedsignal and delay is calculated by considering that the power of thesignal received by the MS decreases with the distance, which in turnsmakes the delay increase.

Among the others, K (P_(R)) depends on (A_(B,0), n_(B,0)) on the directlink, and (A_(R,1), n_(R,1)) on the indirect link. The value of suchparameters can be derived for example from the basic Okumura-Hata modelas described in Y. Okumura et al., “Field Strength and Its Variabilityin UHF and VHF Land-mobile Radio Service”, Rev, Elec. Commun. Lab., vol.16, 1968. Typical values in an urban environment, for a BTS antennaheight of 50 metres and an MS height of 1.5 meters are 123.3 and 33.7,respectively. It is possible to include in A_(B,0) (or in A_(R,1)) anadditional term to take into account the additional path-loss due to thepenetration of radio waves inside buildings. The Referecnce ETSI,Technical Report “Digital cellular telecommunications system (Phase 2+);Radio network planning aspects (GSM 03.30 version 8.3.0 Release 1999), ”doc. ETSI TR 101 362 V8.3.0 (2000-04) suggests to use for thisadditional teim 10 dB in rural and suburban environments and 15 dB inurban environment.

η depends on the uncertainties in the log-distance path-loss attenuationmodel; thus it represents the fluctuations of the propagation delay dueto the propagation over the mobile radio channel.

Usually u₀ and u₁ are modelled as log-normal random variables asillustrated in W. C. Y. Lee, Mobile Cellular Telecommunications Systems,McGraw-Hill Book, 1990. The random variables are u_(o)˜N(0,σ₀) andu₁˜N(0,σ₁). Under this assumption, the probability density function(PDF) of η can be calculated with standard RV transformation techniquesas illustrated in A. Papoulis, Probability, Random Variables, andStochastic Processes—3^(rd) Ed., McGraw-Hill, 1991.

$\begin{matrix}{{f_{\eta}(y)} = {\frac{1}{\sqrt{2\pi\;\sigma}}\frac{n}{y\;\ln\; 10}{\mathbb{e}}^{{{- {({n\;\log_{10}y})}^{2}}/2}\sigma^{2}}{u(y)}}} & (14)\end{matrix}$Where u(y) is the “step function” (equal to 1 if y is positive and equalto zero otherwise), (n,σ) represent (n_(B,0), σ₀ ^(u)) under hypothesisH₀ and (n_(R,1), σ₁ ^(u)) under hypothesis H₁ The corresponding expectedvalue and variance of η areμ_(η)=E{η}=e^((ln10/n)) ² ^(/(σ) ² ^(/2))   (15)σ_(η) ² =E{(η−μ_(η))² }=e ^((ln10/n)) ² ^(/σ) ² (e ^((ln10/n)) ² ^(/σ) ²−1)  (16)

ν represents the fluctuations in the propagation delay observations (ε₀and ε₁) and, in case of connection through the indirect link, also therandom fluctuations of the repeater internal delay (δ_(R)).

When considering the application of this method to a GSM system, thepropagation delay measurements are made available by the parameterTiming Advance (TA). This means that the error contributions ε₀, ε₁include the error made when the TA is used as an estimate of thepropagation delay (or alternatively, of the absolute distance) betweenserving BTS and MS. A statistical characterization of such error hasproved to be important also to implement LCS location algorithms basedon Cell Identity (CI) and Timing Advance (TA), for example. Thus, theneed of statistical information about ε₀ and ε₁ to detect the presenceof a repeater in LCS applications does not represent a problematicissue, since such data is already available to estimate the MScoordinates. Alternatively according to embodiments of the presentinvention equipment for calculating these values may be provided in thecommunication system. The statistics of ε₀ and ε₁ depend heavily on theenvironment and changes also with the value of TA. Depending on theenvironments, average values for ε₀ and ε₁ may vary between −0.75 μs and0.75 μs (corresponding to distances in the range −400 to 400 meters).The standard deviation is commonly about 0.75-1.7 μs (corresponding to400-500 meters).

In the following it is explained how, using classical hypothesis testingtechniques, the repeater detection problem can be solved. Techniques forhypothesis testing of the mean are considered. In order to applyhypothesis testing techniques to the mean value of X, the mean value ofX under hypothesis H₀ (μ₀) and the standard deviation of X underhypothesis H₀ (σ₀) should be determined.

The average value of X defined in (13) under hypothesis H₀ and underhypothesis H₁ can be expressed as follows:

$\begin{matrix}{\mu = {{E\left\{ X \right\}} = \left\{ \begin{matrix}{{{{K\left( {P_{R}❘H_{0}} \right)} \cdot E}\left\{ {\eta ❘H_{0}} \right\}} + {E\left\{ ɛ_{0} \right\}}} & {{if}\mspace{14mu} H_{0}} \\{{{{K\left( {P_{R}❘H_{1}} \right)} \cdot E}\left\{ {\eta ❘H_{1}} \right\}} + {E\left\{ ɛ_{1} \right\}} + {E\left\{ \delta_{R} \right\}} + \tau_{B,R} + \tau_{R}} & {{if}\mspace{14mu} H_{1}}\end{matrix} \right.}} & (18)\end{matrix}$Where E{.} is the expected value and K(P_(R)|H₀ and K(P_(R)|H₁) can befound in table 3 and

$\begin{matrix}\left\{ \begin{matrix}{{E\left\{ {\eta ❘H_{0}} \right\}} = {\mathbb{e}}^{{({\ln\;{10/n_{B,0}}})}^{2}/{({\sigma_{0}^{u^{2}}/2})}}} \\{{E\left\{ {\eta ❘H_{1}} \right\}} = {\mathbb{e}}^{{({\ln\;{10/n_{R,1}}})}^{2}/{({\sigma_{1}^{u^{2}}/2})}}}\end{matrix} \right. & (19)\end{matrix}$

The knowledge of the variance of X affects the selection of thehypothesis testing technique. As mentioned above two classes of testexist. One assumes that the variance of the RV X is known priorcollecting the observations, the other one assumes that the variance isunknown prior to collecting the observations and thus needs to beestimated from the observations themselves. If the variance is known apriori the test statistics (33) is used. If the variance of X is notknown a priori the test statistics (37) is used.

The variance can be pre-determined by taking measurements when settingup the communication system or by calculating it analytically. In theexample considered here (in which a test is performed according toFormulation A, using propagation delay observations) the variance of theobservation X under hypothesis H₀ and under hypothesis H₁ has thefollowing analytical expression, obtained assuming that η and ν areindependent, as well as ε₁ and δ_(R):

$\begin{matrix}{\sigma^{2} = {{{Var}\left\{ X \right\}} = {{E\left\{ \left( {X - \mu} \right)^{2} \right\}} = \left\{ {\begin{matrix}{{{{K^{2}\left( {P_{R}❘H_{0}} \right)} \cdot {Var}}\left\{ {\eta ❘H_{0}} \right\}} + {{Var}\left\{ ɛ_{0} \right\}}} \\{{{{K^{2}\left( {P_{R}❘H_{1}} \right)} \cdot {Var}}\left\{ {\eta ❘H_{1}} \right\}} + {{Var}\left\{ ɛ_{1} \right\}} + {{Var}\left\{ \delta_{R} \right\}}}\end{matrix}{where}} \right.}}} & (20) \\\left\{ \begin{matrix}{{{Var}\left\{ {\eta ❘H_{0}} \right\}} = {{\mathbb{e}}^{{({\ln\;{10/n_{B,0}}})}^{2}/{(\sigma_{0}^{u^{2}})}}\left( {{\mathbb{e}}^{{({\ln\;{10/n_{B,0}}})}^{2}/\sigma_{0}^{u^{2}}} - 1} \right)}} \\{{{Var}\left\{ {\eta ❘H_{1}} \right\}} = {{\mathbb{e}}^{{({\ln\;{10/n_{R,1}}})}^{2}/{(\sigma_{1}^{u^{2}})}}\left( {{\mathbb{e}}^{{({\ln\;{10/n_{R,1}}})}^{2}/\sigma_{1}^{u^{2}}} - 1} \right)}}\end{matrix} \right. & (21)\end{matrix}$

If the variance is not pre-determined or else if a large (for examplegreater than 30) number of readings are available, equation (38) can beused to estimate the variance of X from the sample observation.

Under hypothesis H₀ the analytic expressions of average value andvariance of the propagation delay observation are thus

$\begin{matrix}{\mu_{0} = {{E\left\{ {X❘H_{0}} \right\}} = {{\frac{1}{c^{0}}10{\frac{P_{T,B} - P_{R} - A_{B,0}}{n_{B,0}} \cdot {\mathbb{e}}^{{({\ln\;{10/n_{B,0}}})}^{2}/{({\sigma_{0}^{u^{2}}/2})}}}} + {E\left\{ ɛ_{0} \right\}}}}} & (22) \\{\sigma_{0} = {{{Var}\left\{ {X❘H_{0}} \right\}} = {{\left( {\frac{1}{c_{0}}10^{\frac{P_{T,B} - P_{R} - A_{B,0}}{n_{B,0}}}} \right)^{2} \cdot {{\mathbb{e}}^{{({\ln\;{10/n_{B,0}}})}^{2}/{(\sigma_{0}^{u^{2}})}}\left( {{\mathbb{e}}^{{({\ln\;{10/n_{B,0}}})}^{2}/\sigma_{0}^{u^{2}}} - 1} \right)}} + {{Var}\left\{ ɛ_{0} \right\}}}}} & (23)\end{matrix}$

These values take into account design parameters (P_(T,B)), statisticalproperties of the propagation delay measurement error (ε₀), propertiesof the propagation channel (c₀, A_(B,0), n_(B,0), σ₀ ^(u)). Depending onthe cases (for example if analytic expression for the variance isavailable, then it can be used. If it is not available or it is notreliable, then it can be pre-determined through experimentalmeasurements. Finally, it the variance cannot be pre-determined in anyway, then it must be estimated from the observations.) it may be moreconvenient to apply the hypothesis test method assuming that thevariance is known (in this case the variance would be given byexpression 23 and the technique described hereinabove for known varianceshould be used) or unknown (in this case the variance would be estimatedfrom the set of observations and the technique described hereinabove forunknown variance should be used.).

The alternative hypothesis is then chosen among three possiblealternatives; H₁: μμ₀, H₁: μ>μ₀and H₁: μ<μ₀. Which alternativehypothesis should be chosen, depends on the particular application. Inth example described (test performed according to Formulation A, usingpropagation delay observations) one way to proceed in the selection ofthe alternative hypothesis is to compare the value of μ. underhypothesis H₀ and the value of μ when hypothesis H₀ does not hold. Thedifference (μ|H₁)-(μ|H₀) can be considered for this purpose. This isbecause this quantity is a comparison “of μ under hypothesis H₀ and thevalue of μ when hypothesis H₀ does not hold” from equation (18) itresults that:

$\begin{matrix}{{\left( {\mu ❘H_{1}} \right) - \left( {\mu ❘H_{0}} \right)} = {{{{K\left( {P_{R}❘H_{1}} \right)} \cdot E}\left\{ {\eta ❘H_{1}} \right\}} - {{{K\left( {P_{R}❘H_{0}} \right)} \cdot E}\left\{ {\eta ❘H_{0}} \right\}} + {E\left\{ ɛ_{0} \right\}} - {E\left\{ ɛ_{1} \right\}} + {E\left( \delta_{R} \right\}} + \tau_{B,R} + \tau_{R}}} & (24)\end{matrix}$

Specific considerations should be made case by case. However, byassuming the same propagation parameters for the link between donor BTSand MS (on the direct link) and between Repeater and MS (on the indirectlink), the following simplifications result: E{∈₀}=E {∈,} and E{η|H₁}:in fact, c₀ =c₁=c (where c is the speed of propagation of the radiowaves). A_(B,0)=A_(R,1)=A; n_(B,0)=n_(R,1)=n and σ₀ ^(u)=σ₁ ^(u).Moreover, by assuming E{δ_(R)}=0 then (μ|H_(.1))-(μ|H_(.0)) turns out tohave the following expression:

$\begin{matrix}{\;{{\left( \mu \middle| H_{1} \right) - \left( \mu \middle| H_{0} \right)} = {{{{\left\lbrack {{K\left( P_{R} \middle| H_{1} \right)} - {K\left( P_{R} \middle| H_{0} \right)}} \right\rbrack \cdot E}\left\{ \eta \right\}} + \tau_{B,R} + {\tau_{R}\mspace{211mu}(25)}}\mspace{191mu} = {{\frac{1}{c}10^{\frac{P_{R -}A}{n}}{{10^{\frac{P_{T,B}}{n}}\left\lbrack {- 10^{\frac{P_{T,D} - L_{B,R} + G_{R}}{n}}} \right\rbrack} \cdot E}\left\{ \eta \right\}} + \tau_{B,R} + {\tau_{R}\mspace{95mu}(26)}}}}} & \;\end{matrix}$

In the case of a system where the Repeater is receiving the signaldirectly from the BTS antenna (which thus coincides with the BTS donorantenna), P_(T,B)=P_(T,D). Moreover, if the attenuation on the linkbetween donor BTS antenna and Repeater donor antenna is balanced(L_(B,R)=G_(R)) the terms between parenthesis cancel out and thedifference between average values is simply given by:(μ|H ₁)−(μ|H ₀)=τ_(B,R)−τ_(R)   (27)

Thus (μ|H₁)≧(μ, H₀) and the alternative hypothesis H₁: μ>μ₀ should beselected for the test. Since in the example considered here the nullhypothesis H₀ is “MS connected through direct link”, the alternativehypothesis H₁ is “MS not connected through direct link” and theobservation X represents a propagation delay, the alternative hypothesisis certainly H₁: μ>μ₀. This is because under alternative hypothesis theMS is expected to be connected through the repeater, which, due to itsinternal delay, increases the average value of the observed propagationdelay.

Following a dual reasoning, the alternative hypothesis H₁: μ<μ₀ would beselected if Formulation B was used. In fact in Formulation B μ₀represents the average propagation delay under the assumption that theMS is connected through indirect link (null hypothesis H₀). If thatassumption does not hold (i.e., if H₁ holds: the MS is not connectedthrough repeater) the average propagation delay is expected to be lowerthan μ₀, thus H₁: μ<μ₀ should be selected.

FIG. 4 illustrates the selection of normal and t-distributions whentesting a claim about the population mean. At step S401 the selection isbegun. The first question asked is whether the number of samples n islarge enough (for example, n is greater than 30). This is step S402. Ifthe number of sample measurements is large enough (for example, n isgreater than 30) then equation 37 is used. This is used regardless ofwhether the variance σ is used since it will more accurately provide ananswer. This is step S403. If the number n is not large enough (forexample n is less than or equal to 30) the question of whether thevariance σ is known is asked at step S404. If the variance is not knownthen equation 37 is used to calculate the test statistic Q at step S405.Otherwise equation 33 is utilized for the test statistic at step S406.

In each of equations 37 and 33 the value μ₀ which represents the averagevalue of the population under hypothesis H0. Such value can becalculated using the formula given by equation 22 and by substitutingtherein values of the system such as transmitted power and attenuationeffects as above described. The variance σ can likewise be calculatedfor use with equation 33 using equation 23. Alternatively when equation37 is used the variance or spread is given by S shown in equation 38which may be calculated from the population sample.

It will be understood that the values for the variance and expectedvalue under hypothesis H₀ (μ₀, σ₀) may be calculated from systemparameters using equations analogous to 22 and 23 or may be determinedexperimentally when other formulations of the hypothesis test are used.

Having determined a value for the test statistic via either equation 33or 37 this is compared with the critical region under the particularalternative hypothesis selected. In the above described specific examplethe alternative hypothesis H₁: μ>μ₀ is described as being the bestpossible test. It will be understood that other alternative hypothesisfor testing the null hypothesis could be used if, for instance,Formulation B was used and/or received signal power observations wereused instead of propagation delay observations.

If the test statistic value falls within the critical region, asdetermined for the particular level of certainty α chosen then one cansay that the two values, for the mean, that is the expected value andthe measured sample value, vary by an amount which is statisticallysignificant. That is to say the difference is not likely to be duemerely to the random fluctuations but is likely to be to adiscontinuity. The null hypothesis, that the signal receives the signalsvia a direct link, must be rejected and the MS cannot be assumed beingconnected to the serving BTS through a direct link.

It will be understood that the present invention is equally applicableto use with the null hypothesis that the MS receives signals via anindirect link (Such as by using Formulation B above) and/or by usingreceived signal power observations.

FIG. 5 illustrates a MS 100 in which functionality to enable the abovedescribed embodiments to be put into practice, could be stored. It willbe understood of course that such functionality could be stored in anyother suitable network element. For example in the LMU or SMLC. The MS100 includes a display 500 and buttons 501, 502 which together withother buttons, microphone and earphone (not shown) comprise a userinterface. In FIG. 6 the MS has been cut away to show a data store 503and control apparatus 504.

The data store 503 stores the various hypothesis testing algorithms anddetails of the equations needed to enable the mean values and varianceof sample measurements to be calculated.

It will be understood that the method described hereinabove is generallyapplicable and that alternative implementations can be considered tosuit particular cases without departing from the scope of the presentinvention. For example according to embodiments of the present inventionby observing FIG. 2 it can be seen that outside of the shaded region,indicating the border between BTS coverage area and Repeater coveragearea (i.e., for d>d_(B)), the propagation delay information alone isenough to determine whether the MS is in the BTS coverage area or in theRepeater coverage area.

In these circumstances, the repeater detection problem can beimplemented by first using a reduced test that decides whether the MS isin the border region or not on the basis of propagation delayobservations only. Afterwards, only if the MS turns out to be in theborder region are propagation delay and received level observations usedjointly in a complete test.

The reduced test is a test for the mean value of the propagation delaywith the following hypothesis.

$\left\{ \begin{matrix}{{H_{0}:\mu} = {\mu_{0}^{\prime}\left( {{MS}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{border}} \right)}} \\{H_{1}:{\mu \neq {\mu_{0}^{\prime}\left( {{MS}\mspace{14mu}{not}\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{border}\mspace{14mu}{area}} \right)}}}\end{matrix}\quad \right.$Where μ₀′ is the average value of the propagation delay in the shadedarea 205.

This test determines two thresholds, τ_(H) 208 and τ_(L) 209 such that,if τ_(L)<τ<τ_(H) the hypothesis H₀ is accepted and nothing can be saidyet about the eventual presence of a Repeater. Thereafter the completetest using both propagation delay observations and signal strengthobservations as above described needs to be performed. If τ is smallerthan τ_(L), the MS can be assumed to be within the BTS coverage areawhile if τ>τ_(H), the MS can be assumed within the Repeater coveragearea.

The additional requirement of this implementation is the need to specifyμ₀′ in the reduced test. μ₀′ would need to be specified using additionalinformation not embedded in the observations. For example, μ₀′ can bedetermined from the network design parameters or obtained viaexperimental measurements. μ₀′ depends on the radius of the BTS coveragearea, the Repeater's internal delay and properties of the propagationdelay random fluctuations. In the complete test it is not needed tospecify μ₀′ because signal strength observations carry intrinsically anindication of the average expected propagation delay.

FIG. 4 represents one case where the method and apparatus of embodimentsof the present invention can be adapted to uniquely identify therepeater. In the configuration presented, the donor BTS 101 is connectedto two repeaters 130, 131 installed at exactly the same distance fromthe BTS (d₁=d₂). In these circumstances, if the two indirect links (fromdonor BTS to Repeater 1 and from donor BTS to Repeater 2) are identical,and the repeaters are identical, even though the method so far proposedis able to detect the presence of a repeater from the observations, theparticular configuration does not allow for the determination of fromwhich one of the two repeaters the signal is actually coming.

Under these circumstances one possible way to overcome this limitationis to exploit the eventually available measurements performed by the MSfrom neighbour cells. If the algorithm determines that the MS isconnected to the donor BTS through a repeater, even the identity of theneighbour cells alone may be used to indicate what is the geographicalregion where the MS is located. In such circumstances, the repeaterclosest to the region where the neighbour cells are located can beselected.

Embodiments of the present invention need several parameters in order tobe implemented. Many parameters are likely to be available from radionetwork databases (transmission powers, repeater's internal delay andgain, etc.). Some others need to be determined for each specificimplementation and in some particular circumstances may even vary withthe time. For example, when the link between donor BTS and a repeater isthrough a leased cable, the mobile network operator does not necessarilyknow what are the delay and attenuation characteristics affecting theconnection between donor BTS and repeater. In these cases alternativeways to determine unknown parameters must be devised.

One possibility according to embodiments of the present invention is toinstall test MS's in known locations and use them as reference receiversto determine unknown design parameters. These handsets may be normallyin idle mode when they perform neighbour measurements and periodicallymay be set in dedicated mode. The RXLEV and TA measurements collectedfrom them can be used to determine unknown parameters such as cabledelay and attenuation but also statistical information on the randomfluctuations affecting path-loss and propagation delay.

Embodiments of the present invention provide the advantage that they canbe easily extended to those cases where a chain of repeaters isconnected to one single donor BTS.

1. A method for determining a location of a device communicating with acommunication system, the method comprising: collecting a plurality ofvalues of a first signal characteristic, the first signal characteristicassociated with a propagation delay of a signal received at a firstdevice from a base station; calculating a sample mean value based on thecollected plurality of values; calculating an expected mean value of thefirst signal characteristic; calculating a test statistic based on thecalculated sample mean value and the calculated expected mean value;applying the calculated test statistic to a hypothesis test decisionrule; and determining whether or not the signal received at the firstdevice is received directly from the base station or is received from asecond device based on application of the calculated test statistic toenable an accurate determination of a beat on of the first device. 2.The method of claim 1, further comprising calculating a sample standarddeviation value based on the collected plurality of values wherein thetest statistic is further based on the calculated sample standarddeviation value.
 3. The method of claim 2, wherein calculating thesample standard deviation value is performed only if a number of thecollected plurality of values exceeds a pre-determined threshold.
 4. Themethod of claim 2, wherein calculating the sample standard deviationvalue is performed only if an expected standard deviation value of thefirst signal characteristic is not known.
 5. The method of claim 1,farther comprising calculating an expected standard deviation value ofthe first signal characteristic wherein the test statistic is furtherbased on the calculated expected standard deviation value.
 6. the methodof claim 1, further comprising: determining a first threshold, the firstthreshold defining a propagation delay indicating the signal is receiveddirectly from the base station; if the calculated sample mean value isless than the determined first threshold, determining that the signalreceived at the first device is received directly from the base station.7. The method of claim 1, further comprising: determining a firstthreshold, the first threshold defining a propagation delay indicatingthe signal is not received directly from the base station; if thecalculated sample mean value is greater than the determined firstthreshold, determining that the signal received at the first device isreceived from the second device.
 8. The method of claim 1, wherein thetest statistic has a Gaussian distribution or a t-student distribution.9. The method of claim 1, wherein a null hypothesis of the hypothesistest decision rule determines if the signal received at the first deviceis received directly from the base station,
 10. The method of claim 1,wherein a null hypothesis of the hypothesis test decision ruledetermines if the signal received at the first device is received fromthe second device.
 11. The method of claim 1, wherein the calculatedexpected mean value is based on a first delay associated with the seconddevice and a second delay associated with an attenuation of the signalreceived.
 12. A method for determining a location of a devicecommunicating with a communication system, the method comprising:collecting a plurality of values of a first signal characteristic, thefirst signal characteristic associated with a measured power of a signalreceived at a first device from a base station; calculating sample meanvalue based on the collected plurality of values; calculating anexpected mean value of th first signal characteristic; calculating atest statistic based on the calculated sample mean value and thecalculated expected mean value; applying the calculated test statisticto a hypothesis test decision rule; and determining whether or not thesignal received at the first device is received directly from the basestation or is received from a second device based on application of thecalculated test statistic to enable an accurate determination of alocation of the first device.
 13. The method of claim 12, furthercomprising calculating a sample standard deviation value based on thecollected plurality of values wherein the test statistic is furtherbased on the calculated sample standard deviation value.
 14. The methodof claim 13, wherein calculating the sample standard deviation value isperformed only if a number of the collected plurality of values exceedsa pre-determined threshold.
 15. The method of claim 13, whereincalculating the sample standard deviation value is performed only if anexpected standard deviation value of the first signal characteristic isnot known.
 16. The method of claim 12, further comprising calculating anexpected standard deviation value of the first signal characteristicwherein the test statistic is further based on the calculated expectedstandard deviation value.
 17. The method of claim 12, furthercomprising: determining a first threshold, the first threshold defininga propagation delay indicating the signal is received directly from thebase station; if the calculated sample mean value is less than thedetermined first threshold, determining that the signal received at thefirst device is received directly from the base station.
 18. The methodof claim 12, further comprising: determining a first threshold, thefirst threshold defining a propagation delay indicating the signal isnot received directly from the base station; if the calculated samplemean value is greater than the determined first threshold, determiningthat the signal received at the first device is received from the seconddevice.
 19. The method of claim 12, wherein null hypothesis of thehypothesis test decision rule determines it the signal received at thefirst device is received directly from the base station.
 20. The methodof claim 12, wherein a null hypothesis of the hypothesis test decisionrule determines if the signal received at the first device is receivedfrom the second device.